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[x][x][x][x][x]You threaten the X's
Huh, that's weird, usually doesn't look so odd when I do that. eh, you get the idea. You threaten any square that is 2 squares away from yours.
That's with a reach weapon. A creature with 10 foot natural reach would threaten the ones adjacent as well.

ruemere |
Scipion,
you seem to be confusing certain weapons' reach rules with creature reach rules.
From Pathfinder PRD, Combat:
From Pathfinder PRD, Equipment:Threatened Squares: You threaten all squares into which you can make a melee attack, even when it is not your turn. Generally, that means everything in all squares adjacent to your space (including diagonally). An enemy that takes certain actions while in a threatened square provokes an attack of opportunity from you. If you're unarmed, you don't normally threaten any squares and thus can't make attacks of opportunity.
Reach Weapons: Most creatures of Medium or smaller size have a reach of only 5 feet. This means that they can make melee attacks only against creatures up to 5 feet (1 square) away. However, Small and Medium creatures wielding reach weapons threaten more squares than a typical creature. In addition, most creatures larger than Medium have a natural reach of 10 feet or more.
Reach Weapons: Glaives, guisarmes, lances, longspears, ranseurs, and whips are reach weapons. A reach weapon is a melee weapon that allows its wielder to strike at targets that aren't adjacent to him. Most reach weapons double the wielder's natural reach, meaning that a typical Small or Medium wielder of such a weapon can attack a creature 10 feet away, but not a creature in an adjacent square. A typical Large character wielding a reach weapon of the appropriate size can attack a creature 15 or 20 feet away, but not adjacent creatures or creatures up to 10 feet away.
Regards,
Ruemere